ILASS Americas 27th Annual Conference on Liquid Atomization and Spray Systems, Raleigh, NC, May 2015

Non-Newtonian Impinging Jet Spray Formation at Low Generalized Bird-Carreau Jet Reynolds Numbers

N. S. Rodrigues*, V. Kulkarni, J. Gao, J. Chen, and P. E. Sojka M.J. Zucrow Laboratories

School of Mechanical Engineering Purdue University

West Lafayette, IN 47906 USA

Abstract Non-Newtonian impinging jet spray formation was experimentally investigated using two different grades of Car-

boxymethylcellulose (CMC) mixed with deionized (DI) water (0.5 wt.-% CMC-7HF, 0.8 wt.-% CMC-7MF, and 1.4 wt.-% CMC-7MF). DI water was also tested as a reference liquid. Experimental rheological data obtained using rotational and capillary rheometers was characterized using the Bird-Carreau rheological model and a generalized Bird-Carreau jet Reynolds number Rej,gen-BC was used to correlate atomization behavior. The resulting sprays were qualitatively and quantitatively studied using shadowgraphy. The general behavior exhibited by Newtonian imping-ing jet atomization was not observed when using non-Newtonian liquids; differences are ascribed to the shear-thinning nature of the non-Newtonian liquids employed. Depending on Rej,gen-BC the observed spray patterns include: perforated sheet, ruffled sheet, tangled web, open rim, and ligament web. The experimentally measured maximum instability wavelength and sheet breakup length were observed to decrease with increasing Rej,gen-BC.

*Corresponding author: neilrodrigues@asme.org

ILASS Americas 27th Annual Conference on Liquid Atomization and Spray Systems, Raleigh, NC, May 2015

Introduction Adding a non-Newtonian agent to a liquid with

typical Newtonian properties transforms the liquid into one exhibiting non-Newtonian behavior. Newtonian liquids have a constant value for viscosity independent of strain rate, whereas the viscosity of non-Newtonian liquids varies with strain rate. The ability of shear-thinning, non-Newtonian liquids to not flow easily un-less under pressure is desirable for applications such as liquid rocket propulsion, since containment and cleanup would be more manageable in the event of an accident. Non-traditional liquids for use with aerospace propul-sion systems have been investigated for decades [1]. One main disadvantage of non-Newtonian liquids, however, is the difficulty in atomization due to the in-creased effective viscosity of the liquid [2]. Non-Newtonian agents can generally be divided into two groups: organic and inorganic [3].

The Bird-Carreau model is a suitable choice to ac-count for shear-thinning behavior of liquids that do not have a yield stress, because it can adequately capture the details of the experimentally measured viscosity. The expression for the Bird-Carreau model is:

. (1)

In the above equation η(! ̇)BC is the effective viscosity as a function of the strain rate ! ̇. Zero- and infinite-strain rate viscosity limits are symbolized by η0 and η∞ re-spectively. The parameter n is called the flow behavior index and describes the rapidly decreasing part of the viscosity curve. The parameter λ describes the fluid time response to a change in strain rate [4].

The general primary atomization behavior for im-pinging jet atomization involves two jets colliding to form a liquid sheet. Instabilities on the sheet cause it to fragment into ligaments, which then breakup into drops. The dimensionless parameters that are used for imping-ing jet atomization studies are the jet Reynolds number (inertial force to viscous force) and the jet Weber num-ber (inertial force to surface tension force). Due to the strain-rate dependence of viscosity, the Reynolds num-ber must be modified for non-Newtonian liquids. The generalized Reynolds number based on the Bird-Carreau model Rej,gen-BC [5] is used in this work as the primary dimensionless parameter for atomization. The expression for Rej,gen-BC is:

The terms in the above expression are the Bird-Carreau parameters along with the liquid density ρL, jet velocity

Uj, and jet diameter dj. The expression for the jet Weber number Wej is:

. (3)

In the above equation the liquid/air surface tension is symbolized by γ. The Weber number is unaffected from the Newtonian expression because the surface tension does not vary with strain rate.

Spray characterization of jet impingement with Newtonian liquids has been studied extensively in ex-isting literature [6-9]. Four distinct regimes had been identified by Heidmann et al. (1957) [6]: Closed Rim with Drop Formation, Periodic Drop, Open Rim, and Fully Developed [6]. The jet Reynolds number has been observed to have a great effect on the flavor of the breakup process. For instance, in the “Closed Rim” regime, a distinct sheet was formed and drops were shed from the rim of the sheet. In contrast, for the “Ful-ly Developed” regime the sheet was no longer even visible; ligaments and drops were observed to directly emit from the impingement point.

Although the atomization behavior of non-Newtonian liquids has been studied in recent years [10-16], there is still an incomplete understanding regarding the variety of effects that non-Newtonian behavior has on atomization. Furthermore, atomization regimes for non-Newtonian liquids have not been observed to be nearly as clear-cut [15]. The available literature indi-cates an inverse relationship between the jet Reynolds number and atomization characteristics such as maxi-mum instability wavelength and sheet breakup length [10-13].

Chojnacki and Feikema (1995) [16] and Mallory and Sojka (2014) [12, 13] previously conducted inves-tigations on water-based solutions of carboxymethyl-cellulose (CMC). This work seeks to expand under-standing of the atomization behavior of CMC solutions by experimentally investigating the spray patterns and spray characteristics at low generalized Bird-Carreau jet Reynolds numbers. Experimental Apparatus

A low-shear mixer was used in this work to formu-late the non-Newtonian liquids. Special care was taken during the mixing process to ensure homogeneous mix-ing. The solutions were left to stir until they was deter-mined to be homogenous by visual inspection. Two grades of carboxymethylcellulose, CMC-7HF (700 kDa) and CMC-7MF (250 kDa), were used as the non-Newtonian agents. The water based solutions used in this work were: 0.5 wt.-% CMC-7HF, 0.8 wt.-% CMC, and 1.4 wt.-% CMC-7MF. Deionized (DI) water was also tested as a reference liquid. The three CMC solu-tions can be described as homogenous, soluble, and highly viscous liquids.

η !γ( )BC = 1+ λ !γ( )2⎡⎣⎢

⎤⎦⎥

n−12 η0 −η∞( )+η∞

( )

, 12 2

0

Re

83 1 3 114 4

L j jj gen BC n

j

j

U d

Un nn d n

ρ

λ η η η

− −

∞ ∞

=⎛ ⎞⎛ ⎞⎜ ⎟⎛ ⎞+ +⎛ ⎞⎜ ⎟+ − +⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟ ⎝ ⎠⎜ ⎟⎝ ⎠⎝ ⎠⎜ ⎟⎝ ⎠

L j jj

U dWe

ργ

=

. (2)

A rotational rheometer was used to determine the bulk rheological properties at low strain rates. The cone-and-plate configuration (60 mm, 2.025° angle) was used in controlled-rate mode. A 5% tolerance was set for all measurements. The criterion for a data point to be considered valid was three consecutive measure-ments within the tolerance. A Sweep Up test was con-ducted with increasing strain rates. Sweeping the strain rates from lowest to highest values preserved the solu-tion structure during testing. In order to determine if any thixotropic behavior was present, a Sweep Down test was also conducted.

A capillary rheometer was used to determine the viscosity of the investigated solutions at high strain rates. A 0.66 mm capillary die was used for all meas-urements. The pressure drop was recorded once fully developed flow was achieved in order to determine the liquid viscosity at a particular strain rate. The Weissen-berg-Rabinowitsh correction factor as outlined by Mor-rison (2001) [4] was used for all measurements.

A du Noüy ring tensiometer was used to experi-mentally determine the surface tension of all three CMC solutions. The uncertainty in the measurement was calculated based on one standard deviation from a sample size of ten.

The unique experimental facility used to create the impinging jet atomization for this study was identical to the facility used by Rodrigues et al. (2015) [17]. Figure 1 provides a schematic of the facility. Rotational stages were used to set the impingement angle 2θ = 100°. Translation stages were used to set the free jet length-to-orifice diameter ratio x/d0 = 60. Designated tip ele-ments were used to set the internal length-to-orifice diameter ratio L/d0 = 20 and orifice diameter d0 = 0.686 mm. The operating pressure was controlled in order to vary the mean jet velocity Uj. The flow rate from the orifices were measured for test durations of 30 seconds using a stopwatch. Measurements were repeated three times to ensure statistical significance and the mean jet velocity was calculated based on the measured flow rate.

Figure 1. Schematic of experimental apparatus.

Still photography using the shadowgraphy tech-nique with image analysis has been extensively used for atomization studies [7-13]. In this work the imaged were captured in the plane of the sheet formed by the two jets using a CCD camera. A double-pulsed Nd:YAG laser beam provided the back illumination. In order to reduce the coherence of the laser beam, the laser beam was first expanded and then projected to a diffuser. Figure 2 provides a schematic for the shadow-graphy set-up.

The percent uncertainty for the operating condi-tions was calculated using the Kline and McClintock method [18]. Table 1 presents the calculated uncertainty for the generalized Bird-Carreau jet Reynolds number and the jet Weber number. Further details on calculat-ing the uncertainty is provided in Rodrigues [19]. One standard deviation was used as the experimental uncer-tainty for maximum instability wavelength and sheet breakup length measurements. A sample size of ten images was used at each test condition. Results and Discussion.

The Bird-Carreau rheological model was used to characterize the strain-rate dependency of viscosity for the three non-Newtonian viscous liquids. The effective viscosity versus strain rate for 0.5 wt.-% CMC-7HF, 0.8 wt.-% CMC-7MF, and 1.4 wt.-% CMC-7MF are pre-sented in Figures 3 - 5. The Bird-Carreau model satis-factorily characterized the non-Newtonian behavior of the three liquids. For all three non-Newtonian liquids, a Newtonian plateau was observed at very low strain rates. As the strain rate increased, shear-thinning behav-ior was observed. Since a Newtonian plateau at high strain rates was not observed, it was assumed that the infinite strain rate viscosity was that of the base fluid (water). This assumption is commonly used in literature in work such as Madlener and Ciezki (2012) [20]. The viscosity of water was taken to be the literature value of 0.001 Pa-s. Table 2 provides the Bird-Carreau rheologi-cal parameters for all three CMC solutions. Note that

Figure 2. Schematic of Shadowgraph setup [17].

Quantity Uncertainty (%) Rej,gen-BC 6.4

Wej 4.5 Table 1. Experimental uncertainty for present work.

Figure 3. Viscosity versus strain rate for 0.5 wt.-% CMC-7HF.

Figure 4. Viscosity versus strain rate for 0.8 wt.-% CMC-7MF.

for the Newtonian DI water: η0 = η∞ = 0.001 Pa-s and n = 0. Both sweep up and sweep down tests were con-ducted using the rotational rheometer in order to deter-mine the thixotropic nature of the non-Newtonian liq-uids. All three CMC solutions were not observed to show any significant thixotropic behavior.

It was experimentally observed that all three CMC solutions have surface tension values very close to the literature surface tension value of water – 0.0728 N/m. Therefore, for jet Weber number calculations, the sur-face tension of all three liquids was taken to be the sur-face tension of water. The generalized Bird-Carreau jet Reynolds number and jet Weber numbers for the test conditions in this work are presented in Table 3.

Two impinging jets of 0.5 wt.-% CMC-7HF at Rej,gen-BC = 3,580 and Wej = 1,380 were observed to form a liquid sheet bounded by a thick rim, as shown in Figure 6. Instabilities were observed on the liquid sheet. However, these instabilities led to sheet perforations rather than sheet breakup due to the dominating viscous and surface tension forces. Three-dimensional struc-tures that can be described as wavy rims were observed at the regions of perforation. The rim surrounding the sheet was observed to detach into string-like ligaments,

Figure 5. Viscosity versus strain rate for 1.4 wt.-% CMC-7MF.

Parameter 0.5 wt.-% CMC-7HF 0.8 wt.-% CMC-7MF 1.4 wt.-% CMC-7MF η0 [Pa-s] 0.576 ± 0.029 0.0596 ± 0.0030 0.309 ± 0.015 η∞ [Pa-s] 0.001 0.001 0.001 n [-] 0.169 ± 0.008 0.427 ± 0.021 0.397 ± 0.020 λ [s] 0.334 ± 0.017 0.173 ± 0.009 0.324 ± 0.016

Table 2. Bird-Carreau rheological parameters for investigated non-Newtonian solutions.

(a) (c) Figure 6. Perforated sheet pattern of 0.5 wt.-% CMC-7HF at Rej,gen-BC = 3,580 and Wej = 1,380: (a) spray formation, (b) sheet perforation, (c) drop formation.

(a) (b) Figure 7. Ruffled sheet pattern of 1.4 wt.-% CMC-7MF at Rej,gen-BC = 4,320 and Wej = 1,380: (a) spray for-mation, (b) drop formation.

which were then observed to breakup into a few small drops. This atomization behavior was called the perfo-rated sheet pattern.

The spray formation from the collision of two jets of 1.4 wt.-% CMC-7MF at Rej,gen-BC = 4,320 and Wej = 1,380 was observed to be that of a distinct ruffled circu-lar sheet – and therefore called the ruffled sheet pattern. Instabilities were once again observed on the sheet. However, instead of perforations, long ligaments that maintained connectivity with parts of the liquid sheet were observed. The ligaments then experienced breakup into several drops. This spray pattern is shown in Figure 7.

Moderately increasing the inertial force for the 0.5 wt.-% CMC-7HF impinging jets resulted in spray pat-terns that contained tangled ligaments. Figure 8 shows the tangled web patterns at Rej,gen-BC = 5,110 and Wej = 2,760. Instabilities on the liquid sheet led to the for-mation of large three-dimensional structures that re-sembled a tangled web. Downstream from the im-pingement point, long string-like ligaments were ob-served to detach from the web. A few large drops were observed to form from the ligaments. Further increasing the jet Reynolds and Weber numbers to Rej,gen-BC = 6,280 and Wej = 4,120 as shown in Figure 9 and Rej,gen-

BC = 7,040 and Wej = 5,160 as shown in Figure 10, re-sulted in changes to the morphology of the web. At these generalized Bird-Carreau jet Reynolds number and jet Weber number it was somewhat difficult to de-termine where the liquid sheet experienced breakup and where the ligaments began to form. The structures in-side the tangled web were observed to become increas-ingly dense with an increase in Rej,gen-BC and Wej. In addition, by increasing the inertial force a greater num-ber of ligaments and drops were observed downstream of the web.

The spray formation of two impinging jets of 0.8 wt.-% CMC-7MF at Rej,gen-BC = 4,770 and Wej = 1,100 is presented in Figure 11. This atomization behavior was called the open rim pattern. A circular sheet with instability waves was observed near the impingement point. Downstream from the impingement point the sheet was observed to show bow-shaped ligaments that were connected at the sheet centerline. The ligaments were then observed to detach from the sheet and breakup into several drops. Striking similarities can be observed between this spray pattern and the spray

Liquid Rej,gen-BC Wej 0.5 wt.-% CMC-7HF 3.58E+03 - 7.04E+03 1.38E+03 - 5.16E+03 0.8 wt.-% CMC-7MF 4.77E+03 - 7.81E+03 1.10E+03 - 2.76E+03 1.4 wt.-% CMC-7MF 4.32E+03 - 8.10E+03 1.38E+03 - 4.12E+03

DI Water 9.13E+03 1.69E+03

Table 3. Bird-Carreau rheological parameters for investigated non-Newtonian solutions.

(b)

2 mm

2 mm

2 mm

2 mm

1 mm

(a) (b) Figure 8. Tangled web pattern of 0.5 wt.-% CMC-7HF at Rej,gen-BC = 5,110 and Wej = 2,760: (a) spray for-mation, (b) drop formation.

Figure 9. Tangled web pattern of 0.5 wt.-% CMC-7HF at Rej,gen-BC = 6,280 and Wej = 4,120.

Figure 10. Tangled web pattern of 0.5 wt.-% CMC-7HF at Rej,gen-BC = 7,040 and Wej = 5,160.

(a) (b) Figure 11. Open rim pattern of 0.8 wt.-% CMC-7MF at Rej,gen-BC = 4,770 and Wej = 1,100: (a) spray formation, (b) drop formation.

2 mm

1 mm 1 mm

1 mm

1 mm

1 mm

formation of 1.4 wt.-% CMC-7MF at Rej,gen-BC = 4,320 and Wej = 1,380 (Figure 2). Slightly increasing the jet Reynolds and jet Weber numbers for the 0.8 wt.-% CMC-7MF impinging jets to Rej,gen-BC = 5,400 and Wej = 1,380 led to a stark difference in the spray pattern. As shown in Figure 12, the liquid structure that was ob-served at the lower Rej,gen-BC and Wej was now observed to be very unstable. The structure was observed to breakup into bow shaped ligaments, which then experi-enced breakup into many small drops. Interestingly, this pattern was similar to the spray formation pattern of DI water at Rej,gen-BC = 9,190 and Wej = 1,690, which is presented in Figure 13. This DI water pattern is com-monly referred to as the Open Rim pattern in literature.

Increasing the jet Reynolds and jet Weber numbers for the 1.4 wt.-% CMC-7MF impinging jets from Rej,gen-BC = 4,320 and Wej = 1,380 (Figure 7) to Rej,gen-BC = 6,450 and Wej = 2,760 drastically changed the spray formation pattern. As presented in Figure 14, a ligament web with various three-dimensional morphologies was observed. This atomization behavior was called the perforated sheet pattern. It was again difficult to deter-mine where the liquid sheet experienced breakup and where the ligament web began. The ligaments were observed to separate from the web further downstream and eventually drops were formed from the ligaments. Interestingly, a similar spray pattern was observed for the 0.8 wt.-% CMC-7MF jets at Rej,gen-BC = 7,810 and Wej = 2,760, as shown in Figure 15. This is note worthy because even though two different concentrations of polymers were used for the liquid formulation, the gen-eralized Bird-Carreau jet Reynolds number satisfactori-ly accounted for atomization behavior and polymer

Figure 12. Open Rim pattern of 0.8 wt.-% CMC-7MF at Rej,gen-BC = 5,400 and Wej = 1,380.

Figure 13. Open Rim pattern of DI Water at Rej,gen-BC = 9,130 and Wej = 1,690.

Figure 14. Ligament Web pattern of 1.4 wt.-% CMC-7MF at Rej,gen-BC = 6,450 and Wej = 2,760.

Figure 15. Ligament Web pattern of 0.8 wt.-% CMC-7MF at Rej,gen-BC = 7,810 and Wej = 2,760.

1 mm

1 mm

1 mm

2 mm

Figure 16. Ligament web pattern of 1.4 wt.-% CMC-7MF at Rej,gen-BC = 8,100 and Wej = 4,120.

Figure 17. Dimensionless maximum instability wave-length vs. generalized Bird-Carreau jet Reynolds num-ber.

Figure 18. Dimensionless sheet breakup length vs. generalized Bird-Carreau Jet Reynolds number.

concentration itself does not appear to be a discriminat-ing factor. Figure 16 shows the spray pattern of 1.4 wt.-% CMC-7MF at Rej,gen-BC = 8,100 and Wej = 4,120. Further increasing the inertial force resulted in an in-crease in: the denseness of the ligament web, the num-ber of ligaments separating from the web, and the num-ber of drops formed. Note that these are all common characteristics to the spray patterns of the 0.5 wt.-% CMC-7HF impinging jets, but those spray formation were observed to be different. This was believed to be due to CMC-7HF possessing a higher molecular weight compared to the molecular weight of CMC-7MF.

Figure 17 presents the dimensionless maximum in-stability wavelength versus the generalized Bird-Carreau jet Reynolds number. The dimensionless max-imum instability wavelength was generally observed to decrease with increasing Rej,gen-BC. The dimensionless sheet breakup length was also generally observed to decrease with increasing generalized Bird-Carreau jet Reynolds number, as presented in Figure 18. Note that the maximum instability wavelength and the sheet breakup length were made dimensionless by the orifice diameter. Considerable variation was observed in the experimental measurements due to the unsteady nature of the impinging jet spray and one standard deviation was used for the vertical bars in Figures 17 and 18. The trends for both the maximum instability wavelength and the sheet breakup length agreed with previous Newto-nian and non-Newtonian literature [6-13]. Summary and Conclusions

The impinging jet spray formation of three non-Newtonian liquids was investigated in this work. The rheology of the 0.5 wt.-% CMC-7HF, 0.8 wt.-% CMC-

2 mm

7MF, and 1.4 wt.-% CMC-7MF solutions were charac-terized using the Bird-Carreau rheological model. Spray patterns based on the generalized Bird-Carreau jet Reynolds numbers were presented and qualitatively discussed. Depending on Rej,gen-BC the observed spray patterns include: perforated sheet, ruffled sheet, tangled web, open rim, and ligament web. Experimental meas-urements were presented for maximum instability wavelength and sheet breakup length. Both spray char-acteristics were observed to decrease with increasing generalized Bird-Carreau jet Reynolds number. Nomenclature BC Bird-Carreau rheological model d0 orifice diameter [mm] DI Deionized n BC flow behavior index [-] Rej,gen-BC generalized BC jet Reynolds number [-] Uj mean jet velocity [m/s] Wej jet Weber number [-] Xb sheet breakup length [mm] γ liquid/air surface tension [N-m-1] η0 BC zero-rate viscosity [Pa-s] η∞ BC infinite-rate density [Pa-s] λ BC time constant [s] λm maximum instability wavelength [mm] ρL liquid density [kg-m3] Acknowledgements

The research presented in this paper was made pos-sible with the financial support of the U.S. Army Re-search Office under the Multi-University Research Ini-tiative Grant Number W911NF-08-1-0171. N.S. Ro-drigues thanks Prof. Jennifer Mallory for her valuable input during experimental set-up. References 1. Palaszewski, B., Ianovski, L.S., and Carrick, P.,

Journal of Propulsion and Power 14(5):641-648 (1998).

2. Nathan, B. and Rahimi, S., Combustion of Energetic Materials, Begel House, 2001, p. 172-194.

3. Arnold, R., Santos, P.H.S., deRidder, M., Campan-ella, O.H., and Anderson, W., Journal of Propulsion and Power 27(1): 151-161.

4. Morrison, F., Understanding Rheology, Oxford University Press, 2001.

5. Mallory, J.A., and Sojka, P.E., 24th European Con-ference on Liquid Atomization and Spray Systems, Estoril, Portugal, September 2011.

6. Heidmann, M.F., Priem, R.J., and Humphrey, J.C., “A Study of the Sprays Formed by Two Impinging Jets,” National Advisory Committee for Aero-nautics, Technical Note 3835, 1957.

7. Ibrahim, E.A., and Przekwas, E.A., Physics of Flu-ids A: Fluid Dynamics, 3(12): 2981-2987 (1991).

8. Ryan, H.M, Anderson, W.E, Pal, S., and Santoro, R.J., Journal of Propulsion and Power 11(1): 135-145 (1995).

9. Li R., and Ashgriz, N., Physics of Fluids, 18(8) (2006).

10. Baek, G., Kim, S., Han, J., and Kim, C., Journal of Non-Newtonian Fluid Mechanics 166:1272-1285 (2011).

11. Yang, L.J., Fu, Q.F., Qu, Y.Y., Gu, B., and Zhang, M.Z., International Journal of Multiphase Flow 39:37-44 (2012).

12. Mallory, J.A., and Sojka, P.E., Atomization and Sprays 24(5): 431-465 (2014).

13. Mallory, J.A., and Sojka, P.E., Atomization and Sprays 24(6): 525-554 (2014).

14. Rodrigues N.S., and Sojka, P.E., 52nd Aerospace Sciences Meeting, National Harbor, Maryland, Jan-uary 2014.

15. Von Kampen, J., Ciezki, H.K., Tiedt, T., and Madlener, K., 42nd AIAA Joint Propulsion Confer-ence, Sacramento, California, July 2006.

16. Chojnacki, J.T., and Feikema, D.A., 31st AIAA, ASME, SAE, and ASEE Joint Propulsion Confer-ence and Exhibit, San Diego, California, July 1995.

17. Rodrigues, N.S., Kulkarni, V., Gao, J., Chen, J., Sojka, P.E., Experiments in Fluids 56(50) (2015).

18. Kline, S.J., and McClintock, F.A., Mechanical En-gineering 75:3-8 (1953).

19. Rodrigues, N.S., “Impinging Jet Spray Formation Using Non-Newtonian Liquids,” Purdue University M.S. Thesis, 2014.

20. Madlener, K., and Ciezki, H.K., Journal of Propul-sion and Power, 28(1):113-121 (2012).